Abstract
.
Yang-Mills gravity with translational gauge group
T
(4) in flat space-time implies a simple self-coupling of gravitons and a truly conserved energy-momentum tensor. Its consistency with experiments crucially depends on an interesting property that an “effective Riemannian metric tensor” emerges in and only in the geometric-optics limit of the photon and particle wave equations. We obtain Feynman rules for a coupled graviton-fermion system, including a general graviton propagator with two gauge parameters and the interaction of ghost particles. The equation of motion of macroscopic objects, as an
N
-body system, is demonstrated as the geometric-optics limit of the fermion wave equation. We discuss a relativistic Hamilton-Jacobi equation with an “effective Riemann metric tensor” for the classical particles.